Math Stuff -- Kevin Walker
I can be reached at kw_m3 @ canyon23.net.
I work at Microsoft Station Q.
Papers etc.:
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Fermion condensation and super pivotal categories
(with David Aasen and Ethan Lake);
arxiv 1709.01941
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Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies
(with Maissam Barkeshli, Parsa Bonderson, Chao-Ming Jian, Meng Cheng);
arxiv 1612.07792
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Twisted Interferometry: the topological perspective
(with Parsa Bonderson, Lukasz Fidkowski, Michael Freedman);
arxiv 1601.08225
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The centre of the extended Haagerup subfactor has 22 simple objects
(with Scott Morrison);
arxiv 1404.3955
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Twisted Interferometry
(with Parsa Bonderson, Lukasz Fidkowski, Michael Freedman);
arxiv 1306.2379
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Higher categories, colimits, and the blob complex
(with Scott Morrison);
a more concise, less detailed version of the longer blob paper;
to appear in Proceedings of the National Academy of Sciences,
draft version available here;
also arxiv 1108.5386;
also PNAS May 17, 2011 108 (20) 8139-8145 https://doi.org/10.1073/pnas.1018168108
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(3+1)-TQFTs and Topological Insulators
(with Zhenghan Wang);
arxiv 1104.2632
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The Blob Complex
(with Scott Morrison)
math.AT/1009.5025,
but this version (13 Dec 2011) might be more up to date
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Projective Ribbon Permutation Statistics: a Remnant of non-Abelian Braiding in Higher Dimensions
(with Michael Freedman, Matthew B. Hastings, Chetan Nayak, Xiao-Liang Qi, Zhenghan Wang)
physics.mes-hall/1005.0583
or Phys. Rev. B 83, 115132 (2011)
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Man and machine thinking about the smooth 4-dimensional Poincaré conjecture
(with Michael Freedman, Robert Gompf and Scott Morrison)
math.GT/0906.5177
or Quantum Topology Vol. 1 Issue 2 (2010) 171-208
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An orthogonal approach to the subfactor of a planar algebra
(with Vaughan Jones and Dimitri Shlyakhtenko),
math.OA/0807.4146
or
Pacific Journal of Mathematics Vol. 246 (2010), No. 1, 187-197
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On Picture (2+1)-TQFTs
(with Michael Freedman, Chetan Nayak and Zhenghan Wang),
math.QA/0806.1926
or
Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin
(Nankai Tracts in Mathematics, Vol. 12)
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Positivity of the universal pairing in 3 dimensions
(with Danny Calegari and Michael Freedman),
math.GT/0802.3208
or
Jour. Amer. Math. Soc. 23 (2010), no. 1, 107-188
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Fixing the functoriality of Khovanov homology
(with David Clark and Scott Morrison),
math.GT/0701339
or
Geometry & Topology 13 (2009) 1499-1582
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Noncommuting Flux Sectors in a Tabletop Experiment
(with Alexei Kitaev and Gregory W. Moore),
hep-th/0706.3410
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From String Nets to Nonabelions
(with Lukasz Fidkowski, Michael Freedman, Chetan Nayak and Zhenghan Wang),
cond-mat/0610583
or
Commun. Math. Phys. 287, 805-827 (2009)
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Tilted Interferometry Realizes Universal Quantum Computation in the
Ising TQFT without Overpasses
(with Michael Freedman and Chetan Nayak),
cond-mat/0512072
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Towards Universal Topological Quantum Computation in the ν=5/2
Fractional Quantum Hall State
(with Michael Freedman and Chetan Nayak),
cond-mat/0512066
or
Phys. Rev. B 73, 245307 (2006)
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Universal Manifold Pairings and Positivity
(with Michael Freedman, Alexei Kitaev, Chetan Nayak, Johannes K. Slingerland and Zhenghan Wang),
math.GT/0503054
or
Geometry and Topology 9 (2005) 2303-2317
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New TQFT notes: TQFTs [version 1h, 11 May 2006].
This is an early, incomplete draft.
There are notational (and other) inconsistencies, and some parts have not
been proof-read.
Still, it's probably better than nothing.
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A Class of P,T-Invariant Topological Phases of Interacting Electrons
(with Michael Freedman, Chetan Nayak, Kirill Shtengel and Zhenghan Wang),
cond-mat/0307511
or
Annals of Physics 310 (2004) 428-492
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Quantum SU(2) faithfully detects mapping class groups modulo center
(with Michael Freedman and Zhenghan Wang),
math.GT/0209150
or
Geometry and Topology 6 (2002) 523-539
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1991 TQFT notes: "On Witten's 3-manifold Invariants".
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An Extension of Casson's Invariant,
Princeton University Press, 1992, ISBN 0-691-02532-0,
Amazon
or
P.U.P.
(One of these days I'll make a PDF version available here.
In the meantime, someone donated this DjVu version.)
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An extension of Casson's invariant to rational homology spheres,
Bull. Amer. Math. Soc. 22 (1990), 261-267
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Configuration Spaces of Linkages, undergraduate thesis, Princeton University, 1985,
scanned PDF version
I don't necessarily recommend it, but you can also try to decipher my
slides from talks.
At the moment, there are no links to my new art web site.
Let's fix that.